The method of directly correlating Master Points to Category only works when the dragon is not the strongest or only dragon of that "species" that you own (labaled as "uniqueness" in the formula). So when you hatch a new dragon, it will be 1.3x too high, rounded down. That is where the 11 comes from amd also why a level 30 cat 9 has 352 MP instead of the 11x30 (330).
As seemingly convoluted as the formula seems, I have verified on countless occasions that it does produce the correct values. If it was incorrect, I would have pointed that out already and worked on any necessary fixes. I have advocated for displaying the category on the profile for this reason, it can feel VERY complicated at first and even after you start looking into it. Maybe one day we can get that and this headache will go away...maybe.
@b-l Dark Titan is category 10 and War Titan is category 9, thus Dark Titan has higher base stats and follows the same growth curve due to being the same rarity. Therefor, Dark Titan will always be stronger when the same level, stars, and rank.
(note - category refers to the "base stat category" and is used to determine the stats seen in-game. Sadly there is no way to directly determine category, but it can be found from the max stats)
@dragonlove Long story short, when you consider which dragon to use in battle, the power of a dragon's attack that it can use has only a small impact on how much damage it will do. Sadly I had to make it long and complicated as very little is truly known about what factors play large roles in how much damage you do. So I needed to be thorough...and run the risk of confusing people, heck I get confused at times as well xD
tl:dr at the bottom.
Apologies on the long title and the very long post ahead (over 1100 words). It would have been a disservice to not spell out all of the details and simply sum up the results in one or two lines. My goal with this point and more to come is to slowly peel back the cover of the "black box" that SP uses for the battle mechanics, especially when it comes to how much damage a dragon does.
Ranking heroic and mythical dragons relative to one another by their combined attack strength is a commonly used metric by dragon city players when determining how good or bad a dragon is. In this post I will show that the attack power of dragons have little effect on the damage output and that a new metric should be adopted. To show this I will need to prove two things, damage output is uniformly spread and damage difference is minimal. Uniformity of damage spread is necessary to allow for simple comparisons of the means (average). This analysis was done using a level 70 Kratus, using the following attacks: Giant Crack (638 power), War Fist (1500), and Pure Light+ (2100) with 208, 155, and 239 data points respectively.
I will use 3 different charts to show why I am confident that the damage is uniform. Something to consider is damage spread is ten percent of the mean in both directions, resulting in minimum damage being 90% of mean and maximum damage being 110% of mean. The first will be a trend fit using a spreadsheet, showing that the spread is linear across the spectrum. Second will be a scatter plot of each data point inside of a 200 damage window. And third will be a box and whisker plot to show that there are no outliers and each quartile are similar in size.
- Trend Lines – This diagram is graphing the different data points after they have been put in order of increasing value. The data matches very closely with the linear line and there are no visible jumps in the data, this gives evidence that the data is possibly uniform and complete. In excel you are able to have a trend line assigned to the data and it will attempt to assign a function that matches the format that you chose, in this case a linear line. The equation that it found best fit the data is the equation given in the upper left of each equation, the R2 is a means to show how well the equation fits the data. For R2, the higher the better though the cutoff for this varies by the area of study and is well beyond the scope of this post (math of the trend line as well).
- Scatter Plots – At first glance this looks very “scattered” and does not seem to show much, the important aspect from this output is more that there are no glaring omissions. This data is grouped into sets of 200 damage, for example all damage between 80000 and 80200 each give a +1 to the value assigned to that range. As the data range is very large, it is difficult to draw much conclusion from this diagram on its own, but it lends evidence that there is no gaps or skewing of data in any attack.
- Box Plot – The box and whisker plot is a plot to show how the distribution of data, it groups the data into an equal number of data points for each region, so the lowest quarter are in the bottom “whisker” and the highest quarter are in the top “whisker”, with the middle two quarters forming the “box”. If any of the regions had data that was spread out more or less than other regions, it would appear with that section being longer or shorter respectively. The data I present all has similarly sized regions and thus I can conclude that no quartile has a different spread than the rest
With these three things presented, the data is both uniform and complete, allowing the comparison of the means to determine the relative strengths of damage output between attacks.
- Giant Crack – (155 data points)
- Minimum: 68853 (90.26% of mean)
- Maximum: 84061 (110.20% of mean)
- Mean: 76279.6
- War Fist – (208 data points)
- Minimum: 72760 (90.65% of mean)
- Maximum: 88680 (110.48% of mean)
- Mean: 80266.8
- Pure Light+ – (239 data points)
- Minimum: 75644 (90.05% of mean)
- Maximum: 92283 (109.86% of mean)
- Mean: 84004.0
The mean damage outputs will be used to compare the relative damage done between each move.
- 2100 vs 1500 – 84004.0/80266.8 = 1.04656 (4.656% more)
- 2100 vs 638 – 84004.0/76279.6 = 1.10126 (10.126% more)
- 1500 vs 638 – 80266.8/76279.6 = 1.05227 (5.227% more)
From the data above the following conclusions can be reached. A 2100 power attack deals roughly 5% more damage than a 1500 power attack and roughly 10% more than a 638 power attack, while a 1500 power attack deals roughly 5% more than a 638 power attack. This goes against what is often argued on here that high nucleus is much weaker when compared to the high resolution, the damage spread is similar with the best of high resolution being 2300 and worst of high nucleus being 650. With this data, the best attack of high resolution will deal a little over 10% more damage than the worst attack of high nucleus. Therefor, I propose that the metric by which we compare mythical and heroic dragons to be changed to that of considering type coverage and defending element.
Going forward: Current research is being done to test if a trained move inherits any damage boost and determining the impact of dragon power on damage output. No timeline for either of those analysis as they are time consuming.
P.S. As I finish typing this and from having commented about this in the past, I will make a quick note to those of you who want to counter with "But my kratus did 90000 with pure light+ and only 70000 with Giant crack, so there actually is a big difference." I am going to stop you with mentioning that two data points does not prove anything and given the wide range of damage possible, it is meaningless on its own. Enough data points must be used to be able to confidently get the full picture of how the data is distributed, in this case I have a total of 602 data points.
Also, yes this took a long time and a lot of effort to get the data and do this analysis. This was not done overnight.
tl:dr – 2100 attacks deals 10% more than 638 attacks and 5% more than 1500 attacks. Attack power is not a large factor in damage and rankings should be done with consideration of type coverage and defending element.
Very elegant indeed, @Apod! Moving around in the cheap lower tier and obtaining a large roll set to check the game mechanics. Sounds like you're not noob in statistics This is actually what I like most about DC.
Sorry to keep stirring in this caserole, but just because the distribution of the full dataset is uniform doesn't confirm that there are no dependency on position in the dataset (as @Nynaevelan suggests). Did you by any chance do an autocorrelation of the set?
The reason is that they are mutually exclusive, either the spins are predetermined or they are dependent upon position. Also the rolls being dependent upon the position in which they were rolled is contradicted by me acquiring data in the low cost zone (prior to a change in stance by SP) and these results being the same that I achieved as I went up the tower. If the spins were not predetermined then we could have a discussion on how position has an effect on them. Also if they are predetermined, how would the game know when you would be performing the spin, as this would be required for position dependent spins. Maybe you spent more time than normal to acquire a chest on the way up, this would require them to know what path you would take and would be impossible to implement.
So how do I know there is no position dependency? Because it would break the predetermined nature of the spins that this event and game is built around.
lol I like the way you say that but other than giving you the list of die rolls you will get what other benefit would it offer since as you rightly pointed out it is mostly luck that will be the deciding factor in this event type?
Are you referring to what would you gain from knowing your rolls? From the standpoint of SP they could be out of money from those who would not succeed, but try anyways and get close and purchase coins to get the last part. If someone knew they would not make it from the start they would then be more likely to adjust their strategy to go for chests or other objectives. If that is not what you were referring to, then I missed what you were fully asking.
So far I have moved and this time I am getting a good range of rolls other than 1s or 2s. But then as with previous towers I usually get a good number of 3s in the early half of the tower. It is not until I hit the last 3 floors that I usually get bombarded with too many 1s. I am 2 moves away from floor 5 so I am sure my luck is about to run out. Sadly the only floor I might be able to pick up a Detonation chest is on the 6th floor, the others I would need to go out of my way, so I am crossing my fingers and toes that chest has some Detonation orbs in case I do not make it to the top. I still have not decided if I will purchase to make it or not, I will decide that when I get to the last Collection period.
Seeming to getting good rolls early rather than later is correlation and not causation, you are noticing something that is happen at expected times, but they are not related. The spins don't actually change with your position on the tower, this is because they are predetermined. If changing sections had an effect on what the results of the spin were, then it would alter the predetermined aspect and thus the nature of the spins would not be consistent.
Those are both VERY good questions.
- Yes, I have done two studies on the outcomes of the spins and the average from the studies (both with 250 spin samples) was indeed 2 per spin. The number of each result was close and this combined to indicate the the distribution of rolls was uniform.
- The wasted moves were taken into consideration. I only considered how many steps the player had to move each section and the excess did not roll over into a new section.
With those taken into consideration I am confident that my results are representative of the likely results that players will experience. That said, luck plays a GIGANTIC role in this event and thus it is not possible to nail down if someone will succeed or not without using methods that are frowned upon that won't be named.
@gemspender Knowing the top is reachable is not as simple as yes or no. The random distribution of spins means that each player requires a differing amount of coins to reach the top. Most will likely be able to, assuming you collect all sources of coins and do not deviate on the path. I will be writing a python script later to get a confidence interval for how many coins to reach the top and will post the results here.